Understanding Trigonometric Functions and Their Properties

The video tutorial explains the unit circle and its significance in trigonometry. It covers the behavior of trigonometric functions like tan, cot, sec, and cosec as theta changes, particularly focusing on their behavior near key angles like 0, 45, and 90 degrees. The tutorial uses visual aids to demonstrate how these functions behave on the unit circle, emphasizing the concept of asymptotes and the reciprocal nature of sec and cosec.

What is the starting point on the unit circle when measuring angles in radians?

• 0 degrees

• 90 degrees

• 180 degrees

• 360 degrees

As the angle increases, what happens to the tangent function?

• It oscillates

• It increases and then skyrockets

• It decreases

• It remains constant

Why does the tangent function have an asymptote at 90 degrees?

• Because it is a periodic function

• Because it is undefined at 0 degrees

• Because it never intersects the axis

• Because it intersects the axis

What is the relationship between the tangent and cotangent functions?

• They are both decreasing functions

• They are unrelated

• They are inverses

• They are identical

At what angle is the tangent of 45 degrees equal to 1?

• 90 degrees

• 45 degrees

• 60 degrees

• 30 degrees

What is the starting value of the secant function on the unit circle?

• Undefined

• 0

• 1

• Infinity

How does the secant function behave as the angle increases?

• It decreases

• It remains constant

• It approaches zero

• It skyrockets

Why is the cosecant function undefined at 0 degrees?

• Because it is the reciprocal of sine, which is zero at 0 degrees

• Because it is a periodic function

• Because it is a constant function

• Because it is equal to zero

What happens to the cosecant function as the angle approaches 90 degrees?

• It remains constant

• It becomes undefined

• It decreases

• It increases

Why is the unit circle a powerful tool for understanding trigonometric functions?

• Because it is a historical concept

• Because it provides a visual representation

• Because it is only used in advanced mathematics

• Because it simplifies calculations